Students can Download Class 10 Maths Chapter 13 Statistics Ex 13.2 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 10 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.

## Karnataka State Syllabus Class 10 Maths Chapter 13 Statistics Ex 13.2

Question 1.

The following table shows the ages of the patients admitted in a hospital during a year:

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Answer:

The maximum frequency from the given table is f_{i} = 23

∴ Mode class is 35 – 45.

Class size = h = 10,

Lower limit = l = 35

Frequency (f_{1}) of the modal class = f_{1} = 23

Frequency (f_{0}) of the class preceding mode class = 21

Frequency (f_{2}) of the class succeeding mode class =14

Mode = 36.8 years.

Mean: Assumed mean = 40

= 40 – 4.63

= 35.37 years.

Interpretation: Maximum (mode) number of patients admitted in the hospital are of the age 36.8 years, while on an average the age of a patient admitted to the hospital is 35.37 years.

Question 2.

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

Determine the modal lifetimes of the components.

Answer:

Modal class 60 – 80 because it has maximum frequency ∴ f_{1} = 61

l = 60, f_{0} = 52, f_{2} = 38 and h = 20

Modal lifetimes of the components is 65.623 hours.

Question 3.

The following data gives the distribution of total monthly household expenditure of200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

Answer:

Modal class 1500 – 2000 having maximum frequency f_{1} = 40, l = 1500, f_{0} = 24, f_{2} = 33 and h = 500

The modal monthly expenditure of the families is ₹ 1847.83

Mean:

Assumed mean = a = 3250, h = 500

= 3250 – 587.50

= 2662.50

∴ Mean monthly expenditure is ₹ 2662.50

Question 4.

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data.

Interpret the two measures.

Answer:

Modal class is 30 – 35, it has maximum frequency, f_{1} = 10,

l = 30, h = 5, f_{1} = 10, f_{0} = 9 and f_{2} = 3

= 30 + 0.6

= 30.6

∴ Mode of given data is 30.6.

Mean:

Assumed mean = a = 37.5 and

Class size = a = 5

Interpretation: Most states have a student-teacher ratio of 30.6 (mode) and on an average, this ratio 29.2.

Question 5.

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Find the mode of the data.

Answer:

Modal class is 4000 – 5000. It has maximum number of frequencies.

l = 4000, h = 1000, f_{1} = 18, f_{0} = 4 and f_{2} = 9

= 4000 + 608.7

= 4608.7

∴ The mode of the data is 4608.7 runs.

Question 6.

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below.

Find the mode of the data:

Answer:

Modal class is 40 – 50. It has maximum number of frequencies is 20

l = 40, h = 10, f_{1} = 20, f_{0} = 12 and f_{2} = 11

= 40 + 4.7

= 44.7

The mode of the data is 44.7 cars.